Given the three sides and height of a triangle as consecutive integers: x, (x+1), (x+2) and (x+3).The height of the triangle must be x or x+1.

If the height = x, the sides of the triangle are (x+1), (x+2) and (x+3). If the height = (x+1), then the sides of the triangle are x, (x+2) and (x+3).

Using the Pythagorean equations, one can derive cubic equations for three sets of triangles where (x+3) is the hypotenuse of the larger triangle with height and leg of length h, and where the hypotenuse of the smaller triangle, if extended, would intersect the base of the larger triangle.